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When photons of wavelength $λ$ are incident on an isolated sphere suspended by an isolated thread, the corresponding stopping potential is found to be V. When photons of wavelength $λ / 2$ are used the corresponding stopping potential was thrice the above value. If the light of wavelength $λ / 3$ is used, then calculate the stopping potential for this case.

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$\frac{5}{4} \frac{h C}{λ}$

$\frac{5}{2} \frac{h C}{e λ}$

$\frac{h C}{2 e λ}$

$\frac{5}{4} \frac{h C}{e λ}$

answer is C.

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Detailed Solution

$K_{1} = \frac{h C}{λ} - ϕ = e V ...... (i)$

$K_{2} = \frac{2 h C}{λ} - ϕ = e 3 V ...... (i i)$

From (i) and (ii)

$(\frac{h C}{λ} - ϕ) 3 = (\frac{2 h C}{λ} - ϕ)$

$\frac{3 h C}{λ} - 3 ϕ = \frac{2 h C}{λ} - ϕ$

$\frac{h C}{λ} = 2 ϕ \Rightarrow ϕ = \frac{h C}{2 λ} ....... (i i i)$

$\frac{h C}{λ / 3} - ϕ = e V_{0}$

$\frac{h C}{λ / 3} - \frac{h C}{2 λ} = e V_{0}$

$\frac{h C}{λ} (3 - \frac{1}{2}) = e V_{0} \Rightarrow V_{0} = (\frac{5 h C}{2 e λ})$

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